Is 石丽梅 a good Chinese name?

Yes, it is. I mean, since your own name is Mary Shipp, Shi Limei, or 石丽梅 in Chinese, is a good Chinese name for you.

The Chinese surname 石, which means stone, is a commonly seen Chinese surname. There are many people sharing this surname, for instance, Shi Jieru, or 石洁茹 in Chinese, an actress from mainland China, and Shi Anni, or 石安妮 in Chinese, an actress from mainland China.

Here is a picture of Shi Jieru.

Here is a picture of Shi Anni.

The Chinese character 丽 could mean beautiful and gorgeous. And it could be used as a generational name, such as, Teresa Teng, or 邓丽君 (1953–1995) in Chinese, a singer from Taiwan, and Wang Likun, or 王丽坤 in Chinese, an actress from mainland China.

Here is a picture of Teresa Teng.

Here is a picture of Wang Likun.

With regard to the Chinese character 梅, it could mean plum blossom. And 梅 could be used as a female given name, for example, Vivian Wu, or 邬君梅 in Chinese, an actress born and raised in Shanghai and later immigrated to United States, and Zhao Dongmei, or 赵冬梅 in Chinese, a professor of history of Song Dynasty at Peking University.

Here is a picture of Vivian Wu.

Here is a picture of Zhao Dongmei.

So, you see, Shi Limei, or 石丽梅 in Chinese, is a good Chinese name.